The invention relates to a rotary piston machine of the type comprising a housing having a cylindrical main rotor bore and at least one cylindrical auxiliary rotor bore parallel to and intersecting the main rotor bore end walls being provided to close both axial ends of the main and auxiliary bores, a main rotary piston having a generally cylindrical portion of lesser diameter than that of the main rotor bore and coaxial therewith, and a summit portion which extends from the cylindrical portion to engage the wall of the main rotor bore, an auxiliary rotary pistion mounted in the, or each, auxiliary rotor bore and having a profile which is complementary to that of the main rotary piston such that when the pistons are driven at the same speed in the same direction the, or each auxiliary rotary piston is in rotating contact or proximity with the periphery of the main rotary piston. Such a rotary piston machine will herein be referred to as "a rotary piston machine of the type described".